Introduction to attosecond delays in photoionization

This tutorial presents an introduction to the interaction of light and matter on the attosecond timescale.Our aim is to detail the theoretical description of ultra-short time delays and to relate these to the phase of extreme ultraviolet (XUV) light pulses and to the asymptotic phaseshifts of photoelectron wave packets.Special emphasis is laid on time-delay experiments, where attosecond XUV pulses are used to photoionize target atoms at well-defined times, followed by a probing process in real time by a phase-locked, infrared laser field.In this way, the laser field serves as a 'clock' to monitor the ionization event, but the observable delays do not correspond directly to the delay associated with single-photon ionization.Instead, a significant part of the observed delay originates from a measurement induced process, which obscures the single-photon ionization dynamics.This artefact is traced back to a phaseshift of the above-threshold ionization transition matrix element, which we call the continuum-continuum phase.It arises due to the laser-stimulated transitions between Coulomb continuum states.As we shall show here, these measurement-induced effects can be separated from the single-photon ionization process, using analytical expressions of universal character, so that eventually the attosecond time delays in photoionization can be accessed.(Some figures may appear in colour only in the online journal) List of abbreviations APT Attosecond pulse train ATI Above-threshold ionization CEP Carrier envelope phase FROG Frequency-resolved optical gating CRAB Complete reconstruction of attosecond bursts GD Group delay HHG High-order harmonic generation IR Infrared MBPT Many-body perturbation theory RABITT Resolution of attosecond beating by interference of two-photon transitions RPA Random-phase approximation SAE Single-active electron SAP Single-attosecond pulse SB Sideband SFA Strong-field approximation SPA Saddle-point approximation TDSE Time-dependent Schrödinger equation TOF Time-of-flight VMI Velocity-map imaging WKB Wentzel-Kramers-Brillouin XUV Extreme ultraviolet